Question

СРОЧНО! Много баллов. Помогите сократить дроби:


Answer 1

$\frac{x^ \frac{1}{6}-y^ \frac{1}{6} }{x^{ \frac{1}{3} }-y^{ \frac{1}{3} }} = \frac{x^ \frac{1}{6}-y^ \frac{1}{6} }{(x^{ \frac{1}{6} })^2-(y^{ \frac{1}{6}})^2} = \frac{x^ \frac{1}{6}-y^ \frac{1}{6} }{(x^{ \frac{1}{6} }-y^{ \frac{1}{6} })(x^{ \frac{1}{6} }+y^{ \frac{1}{6} })} = \frac{1}{x^{ \frac{1}{6} }+y^{ \frac{1}{6} }}$

$\frac{2-a}{3 \sqrt{2}-3a^ \frac{1}{2} }= \frac{-[(a^ \frac{1}{2})^2- (\sqrt{2})^2] }{-3(a^ \frac{1}{2} - \sqrt{2} )} = \frac{(a ^\frac{1}{2} - \sqrt{2})(a ^\frac{1}{2} + \sqrt{2})}{3(a ^\frac{1}{2} - \sqrt{2})} = \frac{a ^\frac{1}{2} + \sqrt{2}}{3}$

$\frac{a+b}{a^ \frac{2}{3}-a^ \frac{1}{3}b^ \frac{1}{3}+b^ \frac{2}{3} } = \frac{(a^ \frac{1}{3} )^3+(b^ \frac{1}{3} )^3}{a^ \frac{2}{3}-a^ \frac{1}{3}b^ \frac{1}{3}+b^ \frac{2}{3} } = \frac{(a^ \frac{1}{3} +b^ \frac{1}{3} )*[(a^ \frac{1}{3} )^2+a^ \frac{1}{3}b^ \frac{1}{3}+(b^ \frac{1}{3} )^2 ]}{a^ \frac{2}{3}-a^ \frac{1}{3}b^ \frac{1}{3}+b^ \frac{2}{3} } =$
$= \frac{(a^ \frac{1}{3} +b^ \frac{1}{3} )*[a^ \frac{2}{3}-a^ \frac{1}{3}b^ \frac{1}{3}+b^ \frac{2}{3} ]}{a^ \frac{2}{3}-a^ \frac{1}{3}b^ \frac{1}{3}+b^ \frac{2}{3} } =a^ \frac{1}{3} +b^ \frac{1}{3}$